Hawaii
North Dakota
Minnesota
Washington
Oregon
Montana
Wyoming
Nevada
Utah
Arizona
New Mexico
Colorado
South Dakota
Nebraska
Oklahoma
Texas
Iowa
Missouri
Arkansas
Louisiana
Mississippi
Michigan
Illinois
Indiana
Kentucky
Tennessee
Alabama
Florida
Georgia
South Carolina
North Carolina
Virginia
West Virginia
Ohio
Delaware
Maryland
New Jersey
New York
Pennsylvania
Connecticut
Massachusetts
Rhode Island
and Washington D.C.

I've flown over Alaska a few times, but I guess that doesn't really count.

Military posts visited:

Fort Polk, LA
Fort Campbell, KY
Fort Knox, KY
Fort Jackson, SC
Fort Benning, GA
Fort Bragg, NC
Fort Lee, VA
Fort Huachuca, AZ
Fort Rucker, AL
Camp Shelby, MS
Camp McCain, MS
Camp Blanding, FL
Dobbins Air Base, GA
McDill Air Base, FL
Eglin Air Base, FL
Pensacola Naval Air Station, FL

Aquariums visited:

Atlantis Aquarium, NY
The Georgia Aquarium, GA
Aquarium of the Americas, LA
The Florida Aquarium, FL
Sea World, FL
The Baltimore Aquarium, MD
Sunshine Aquarium, Tokyo
Kaukyokan Aquarium, Japan
Osaka Aquarium, Japan
Fukuoka Aquarium, Japan
Churaumi Aquarium, Japan
Busan Aquarium, Korea
Madrid Aquarium, Spain
Qingdao Aquarium, China

Various places or things visited:

Bunaken Marine Sanctuary, Indonesia
Death Valley National Park, CA
Mt. St. Helen, WA
Mt. Ranier, WA
Valley of Fire State Park, NV
Great Salt Lake, UT
Volcanoes National Park, HI
Zion National Park, UT
Bryce Canyon National Park, UT
Grand Canyon National Park, AZ
Petrified Forest National Park, AZ
Badlands National Park, SD
Hot Springs National Park, AR
Big Cypress National Reserve, FL
Carlsbad Caverns National Park, NM
Mammoth Cave National Park, KY
Black Hills National Forest, SD
Fort Sumter National Monument, SC
Devil's Tower, WY
Painted Desert, AZ
Sunset Crater, AZ
Meteor Crater, AZ
Mount Rushmore, SD
Glen Canyon Dam, AZ
Hoover Dam, NV
Kennedy Spaceflight Center, FL
Marshall Spaceflight Center, AL
Stennis Spaceflight Center, MS
The White House, D.C.
The Washington Monument, D.C.
The Jefferson Memorial, D.C.
The Lincoln Memorial, D.C.
The Vietnam Wall, D.C.
The U.S. Capitol, D.C.
Arlington National Cemetery, D.C.
The Smithsonian, Washington D.C.
The Peabody Museum, MA
The American Museum of Natural History, NY
The Statue of Liberty, NY
The Empire State Building, NY
The World Trade Towers, NY
The French Quarter, N.O., LA
Ybor City, Tampa, FL
Talladega Superspeedway, AL
Mount Fuji, Japan
Mount Aso, Japan
Mount Hiko, Japan
Mount Hirodai, Japan
Mount Miyanoura, Japan
Mount Unzen, Japan
Mount Sakurajima, Japan
Yakushima Island, Japan
Kirishima Volcanic Group, Japan
The Imperial Palace Garden, Tokyo
The Tsukiji Fish Market, Ginza, Tokyo
Zojoi Temple, Roppongi, Tokyo
Tokyo Tower, Tokyo (obviously)
Asakusa Kannon Temple, Asakusa, Tokyo
Togo Shrine, Shibuya, Tokyo
Tokyo National Museum
Fukuoka, Japan
Kitakyushu, Japan
Kagoshima, Japan
Hiroshima, Japan
Beppu, Japan
Kyoto, Japan
Kobe, Japan
Osaka, Japan
Okinawa, Japan
The London Tower, London, England
Westminster Abby, London
The Parliament, London
The Imperial War Museum, England
Trafalgar Square, London
St. Paul's Cathedral, London
The Swiss Alps, Switzerland
Lake Geneva, Geneva, Switzerland
D-day Memorial Cemetery, Normandy, France
Pont-du-Hoc, Normandy
Mont St. Michel, Normandy
The Somme, France
Verdun, France
The Eiffel Tower, Paris, France
The Louvre, Paris
The Palace of Versailles, Paris
Notre Dame, Paris
Napoleon's Tomb, Paris
The Columbus Monument, Bahamas
Kilauea Volcano, HI
Mona Loa Volcano, HI